Multiview Clustering Based on Non-Negative Matrix Factorization and Pairwise Measurements

Difference of Convex Functions Programming With Machine-Learning Prior for the Imaging Problem in Electrical Capacitance Tomography

The electrical capacitance tomography technology has potential benefits for the process industry by providing visualization of material distributions. One of the main technical gaps and impediments that must be overcome is the low-quality tomogram. To address this problem, this study introduces the data-guided prior and combines it with the electrical measurement mechanism and the sparsity prior to produce a new difference of convex functions programming problem that turns the image reconstruction problem into an optimization problem. The data-guided prior is learned from a provided dataset and captures the details of imaging targets since it is a specific image. A new numerical scheme that allows a complex optimization problem to be split into a few less difficult subproblems is developed to solve the challenging difference of convex functions programming problem. A new dimensionality reduction method is developed and combined with the relevance vector machine to generate a new learning engine for the forecast of the data-guided prior. The new imaging method fuses multisource information and unifies data-guided and measurement physics modeling paradigms. Performance evaluation results have validated that the new method successfully works on a series of test tasks with higher reconstruction quality and lower noise sensitivity than the popular imaging methods.

Enhanced tensor low-rank representation learning for multi-view clustering

Multi-view subspace clustering (MSC), assuming the multi-view data are generated from a latent subspace, has attracted considerable attention in multi-view clustering. To recover the underlying subspace structure, a successful approach adopted recently is subspace clustering based on tensor nuclear norm (TNN). But there are some limitations to this approach that the existing TNN-based methods usually fail to exploit the intrinsic cluster structure and high-order correlations well, which leads to limited clustering performance. To address this problem, the main purpose of this paper is to propose a novel tensor low-rank representation (TLRR) learning method to perform multi-view clustering. First, we construct a 3rd-order tensor by organizing the features from all views, and then use the t-product in the tensor space to obtain the self-representation tensor of the tensorial data. Second, we use the ℓ_1,2 norm to constrain the self-representation tensor to make it capture the class-specificity distribution, that is important for depicting the intrinsic cluster structure. And simultaneously, we rotate the self-representation tensor, and use the tensor singular value decomposition-based weighted TNN as a tighter tensor rank approximation to constrain the rotated tensor. For the challenged mathematical optimization problem, we present an effective optimization algorithm with a theoretical convergence guarantee and relatively low computation complexity. The constructed convergent sequence to the Karush-Kuhn-Tucker (KKT) critical point solution is mathematically validated in detail. We perform extensive experiments on four datasets and demonstrate that TLRR outperforms state-of-the-art multi-view subspace clustering methods.

Intrinsic Graph Learning With Discrete Constrained Diffusion-Fusion

Graphs are essential to improve the performance of graph-based machine learning methods, such as spectral clustering. Various well-designed methods have been proposed to learn graphs that depict specific properties of real-world data. Joint learning of knowledge in different graphs is an effective means to uncover the intrinsic structure of samples. However, the existing methods fail to simultaneously mine the global and local information related to sample structure and distribution when multiple graphs are available, and further research is needed. Hence, we propose a novel intrinsic graph learning (IGL) with discrete constrained diffusion-fusion to solve the above problem in this article. In detail, given a set of the predefined graphs, IGL first obtains the graph encoding the global high-order manifold structure via the diffusion-fusion mechanism based on the tensor product graph. Then, two discrete operators are integrated to fine-prune the obtained graph. One of them limits the maximum number of neighbors connected to each sample, thereby removing redundant and erroneous edges. The other one forces the rank of the Laplacian matrix of the obtained graph to be equal to the number of sample clusters, which guarantees that samples from the same subgraph belong to the same cluster and vice versa. Moreover, a new strategy of weight learning is designed to accurately quantify the contribution of pairwise predefined graphs in the optimization process. Extensive experiments on six single-view and two multiview datasets have demonstrated that our proposed method outperforms the previous state-of-the-art methods on the clustering task.

Tensorial Multiview Representation for Saliency Detection via Nonconvex Approach

In the study of salient object detection, multiview features play an important role in identifying various underlying salient objects. As to current common patch-based methods, all different features are handled directly by stacking them into a high-dimensional vector to represent related image patches. These approaches ignore the correlations inhering in the original spatial structure, which may lead to the loss of certain underlying characterization such as view interaction. In this article, different from currently available approaches, a tensorial feature representation framework is developed for the salient object detection in order to better explore the complementary information of multiview features. Under the tensor framework, a tensor low-rank constraint is applied to the background to capture its intrinsic structure, a tensor group sparsity regularization is posed on the salient part, and a tensorial sliced Laplacian regularization is then introduced to enlarge the gap between the subspaces of the background and salient object. Moreover, a nonconvex tensor Log-determinant function, instead of the tensor nuclear norm, is adopted to approximate the tensor rank for effectively suppressing the confusing information resulted from underlying complex backgrounds. Further, we have deduced the closed-form solution of this nonconvex minimization problem and established a feasible algorithm whose convergence is mathematically proven. Experiments on five well-known public datasets are provided and the simulations demonstrate that our method outperforms the latest unsupervised handcrafted features-based methods in the literature. Furthermore, our model is flexible with various deep features and is competitive with the state-of-the-art approaches.

Autoweighted Multiview Feature Selection With Graph Optimization

In this article, we focus on the unsupervised multiview feature selection, which tries to handle high-dimensional data in the field of multiview learning. Although some graph-based methods have achieved satisfactory performance, they ignore the underlying data structure across different views. Besides, their predefined Laplacian graphs are sensitive to the noises in the original data space and fail to obtain the optimal neighbor assignment. To address the above problems, we propose a novel unsupervised multiview feature selection model based on graph learning, and the contributions are three-fold: 1) during the feature selection procedure, the consensus similarity graph shared by different views is learned. Therefore, the proposed model can reveal the data relationship from the feature subset; 2) a reasonable rank constraint is added to optimize the similarity matrix to obtain more accurate information; and 3) an autoweighted framework is presented to assign view weights adaptively, and an effective alternative iterative algorithm is proposed to optimize the problem. Experiments on various datasets demonstrate the superiority of the proposed method compared to the state-of-the-art methods.

CSMVC: A Multiview Method for Multivariate Time-Series Clustering

Multivariate time-series (MTS) clustering is a fundamental technique in data mining with a wide range of real-world applications. To date, though some approaches have been developed, they suffer from various drawbacks, such as high computational cost or loss of information. Most existing approaches are single-view methods without considering the benefits of mutual-support multiple views. Moreover, due to its data structure, MTS data cannot be handled well by most multiview clustering methods. Toward this end, we propose a consistent and specific non-negative matrix factorization-based multiview clustering (CSMVC) method for MTS clustering. The proposed method constructs a multilayer graph to represent the original MTS data and generates multiple views with a subspace technique. The obtained multiview data are processed through a novel non-negative matrix factorization (NMF) method, which can explore the view-consistent and view-specific information simultaneously. Furthermore, an alternating optimization scheme is proposed to solve the corresponding optimization problem. We conduct extensive experiments on 13 benchmark datasets and the results demonstrate the superiority of our proposed method against other state-of-the-art algorithms under a wide range of evaluation metrics.

A Multiview Clustering Method With Low-Rank and Sparsity Constraints for Cancer Subtyping

Multiomics data clustering is one of the major challenges in the field of precision medicine. Integration of multiomics data for cancer subtyping can improve the understanding on cancer and reveal systems-level insights. How to integrate multiomics data for accurate cancer subtyping is an interesting and challenging research problem. To capture the global and the local structure of omics data, a novel framework for integrating multiomics data is proposed for cancer subtyping. Multiview clustering with low-rank and sparsity constraints (MVCLRS) can measure the local similarities of samples in each omics data and obtain global consensus structures by integrating the multiomics data. The main insight provided by MVCLRS is that low-rank sparse subspace clustering for the construction of an affinity matrix can best capture the local similarities in omics data. Extensive testing is conducted on 10 real world cancer datasets with multiomics from The Cancer Genome Atlas. Compared with 10 state-of-the-art multiomics clustering algorithms, the MVCLRS performs better in the 10 cancer datasets by providing its clustering results with at least one enriched clinical label in nine of ten cancer subtypes, the most of any method.

Progressive Self-Supervised Clustering With Novel Category Discovery

These days, clustering is one of the most classical themes to analyze data structures in machine learning and pattern recognition. Recently, the anchor-based graph has been widely adopted to promote the clustering accuracy of plentiful graph-based clustering techniques. In order to achieve more satisfying clustering performance, we propose a novel clustering approach referred to as the progressive self-supervised clustering method with novel category discovery (PSSCNCD), which consists of three separate procedures specifically. First, we propose a new semisupervised framework with novel category discovery to guide label propagation processing, which is reinforced by the parameter-insensitive anchor-based graph obtained from balanced K -means and hierarchical K -means (BKHK). Second, we design a novel representative point selected strategy based on our semisupervised framework to discover each representative point and endow pseudolabel progressively, where every pseudolabel hypothetically corresponds to a real category in each self-supervised label propagation. Third, when sufficient representative points have been found, the labels of all samples will be finally predicted to obtain terminal clustering results. In addition, the experimental results on several toy examples and benchmark data sets comprehensively demonstrate that our method outperforms other clustering approaches.

Pseudo-Label Guided Collective Matrix Factorization for Multiview Clustering

Multiview clustering has aroused increasing attention in recent years since real-world data are always comprised of multiple features or views. Despite the existing clustering methods having achieved promising performance, there still remain some challenges to be solved: 1) most existing methods are unscalable to large-scale datasets due to the high computational burden of eigendecomposition or graph construction and 2) most methods learn latent representations and cluster structures separately. Such a two-step learning scheme neglects the correlation between the two learning stages and may obtain a suboptimal clustering result. To address these challenges, a pseudo-label guided collective matrix factorization (PLCMF) method that jointly learns latent representations and cluster structures is proposed in this article. The proposed PLCMF first performs clustering on each view separately to obtain pseudo-labels that reflect the intraview similarities of each view. Then, it adds a pseudo-label constraint on collective matrix factorization to learn unified latent representations, which preserve the intraview and interview similarities simultaneously. Finally, it intuitively incorporates latent representation learning and cluster structure learning into a joint framework to directly obtain clustering results. Besides, the weight of each view is learned adaptively according to data distribution in the joint framework. In particular, the joint learning problem can be solved with an efficient iterative updating method with linear complexity. Extensive experiments on six benchmark datasets indicate the superiority of the proposed method over state-of-the-art multiview clustering methods in both clustering accuracy and computational efficiency.

One-Step Multiview Subspace Segmentation via Joint Skinny Tensor Learning and Latent Clustering

Multiview subspace clustering (MSC) has attracted growing attention due to the extensive value in various applications, such as natural language processing, face recognition, and time-series analysis. In this article, we are devoted to address two crucial issues in MSC: 1) high computational cost and 2) cumbersome multistage clustering. Existing MSC approaches, including tensor singular value decomposition (t-SVD)-MSC that has achieved promising performance, generally utilize the dataset itself as the dictionary and regard representation learning and clustering process as two separate parts, thus leading to the high computational overhead and unsatisfactory clustering performance. To remedy these two issues, we propose a novel MSC model called joint skinny tensor learning and latent clustering (JSTC), which can learn high-order skinny tensor representations and corresponding latent clustering assignments simultaneously. Through such a joint optimization strategy, the multiview complementary information and latent clustering structure can be exploited thoroughly to improve the clustering performance. An alternating direction minimization algorithm, which owns low computational complexity and can be run in parallel when solving several key subproblems, is carefully designed to optimize the JSTC model. Such a nice property makes our JSTC an appealing solution for large-scale MSC problems. We conduct extensive experiments on ten popular datasets and compare our JSTC with 12 competitors. Five commonly used metrics, including four external measures (NMI, ACC, F-score, and RI) and one internal metric (SI), are adopted to evaluate the clustering quality. The experimental results with the Wilcoxon statistical test demonstrate the superiority of the proposed method in both clustering performance and operational efficiency.

Semisupervised Affinity Matrix Learning via Dual-Channel Information Recovery

This article explores the problem of semisupervised affinity matrix learning, that is, learning an affinity matrix of data samples under the supervision of a small number of pairwise constraints (PCs). By observing that both the matrix encoding PCs, called pairwise constraint matrix (PCM) and the empirically constructed affinity matrix (EAM), express the similarity between samples, we assume that both of them are generated from a latent affinity matrix (LAM) that can depict the ideal pairwise relation between samples. Specifically, the PCM can be thought of as a partial observation of the LAM, while the EAM is a fully observed one but corrupted with noise/outliers. To this end, we innovatively cast the semisupervised affinity matrix learning as the recovery of the LAM guided by the PCM and EAM, which is technically formulated as a convex optimization problem. We also provide an efficient algorithm for solving the resulting model numerically. Extensive experiments on benchmark datasets demonstrate the significant superiority of our method over state-of-the-art ones when used for constrained clustering and dimensionality reduction. The code is publicly available at https://github.com/jyh-learning/LAM.

Boolean matrix factorization based on collaborative neurodynamic optimization with Boltzmann machines

This paper presents a collaborative neurodynamic approach to Boolean matrix factorization. Based on a binary optimization formulation to minimize the Hamming distance between a given data matrix and its low-rank reconstruction, the proposed approach employs a population of Boltzmann machines operating concurrently for scatter search of factorization solutions. In addition, a particle swarm optimization rule is used to re-initialize the neuronal states of Boltzmann machines upon their local convergence to escape from local minima toward global solutions. Experimental results demonstrate the superior convergence and performance of the proposed approach against six baseline methods on ten benchmark datasets.

Multiview Spectral Clustering via Robust Subspace Segmentation

Multiview clustering refers to partition data according to its multiple views, where information from different perspectives can be jointly used in some certain complementary manner to produce more sensible clusters. It is believed that most of the existing multiview clustering methods technically suffer from possibly corrupted data, resulting in a dramatically decreased clustering performance. To overcome this challenge, we propose a multiview spectral clustering method based on robust subspace segmentation in this article. Our proposed algorithm is composed of three modules, that is: 1) the construction of multiple feature matrices from all views; 2) the formulation of a shared low-rank latent matrix by a low rank and sparse decomposition; and 3) the use of the Markov-chain-based spectral clustering method for producing the final clusters. To solve the optimization problem for a low rank and sparse decomposition, we develop an optimization procedure based on the scheme of the augmented Lagrangian method of multipliers. The experimental results on several benchmark datasets indicate that the proposed method outperforms favorably compared to several state-of-the-art multiview clustering techniques.

Efficient Unsupervised Dimension Reduction for Streaming Multiview Data

Multiview learning has received substantial attention over the past decade due to its powerful capacity in integrating various types of information. Conventional unsupervised multiview dimension reduction (UMDR) methods are usually conducted in an offline manner and may fail in many real-world applications, where data arrive sequentially and the data distribution changes periodically. Moreover, satisfying the requirements of high memory consumption and expensive retraining of the time cost in large-scale scenarios are difficult. To remedy these drawbacks, we propose an online UMDR (OUMDR) framework. OUMDR aims to seek a low-dimensional and informative consensus representation for streaming multiview data. View-specific weights are also learned in this article to reflect the contributions of different views to the final consensus presentation. A specific model called OUMDR-E is developed by introducing the exclusive group LASSO (EG-LASSO) to explore the intraview and interview correlations. Then, we develop an efficient iterative algorithm with limited memory and time cost requirements for optimization, where the convergence of each update is theoretically guaranteed. We evaluate the proposed approach in video-based expression recognition applications. The experimental results demonstrate the superiority of our approach in terms of both effectiveness and efficiency.

Uniform Distribution Non-Negative Matrix Factorization for Multiview Clustering

Multiview data processing has attracted sustained attention as it can provide more information for clustering. To integrate this information, one often utilizes the non-negative matrix factorization (NMF) scheme which can reduce the data from different views into the subspace with the same dimension. Motivated by the clustering performance being affected by the distribution of the data in the learned subspace, a tri-factorization-based NMF model with an embedding matrix is proposed in this article. This model tends to generate decompositions with uniform distribution, such that the learned representations are more discriminative. As a result, the obtained consensus matrix can be a better representative of the multiview data in the subspace, leading to higher clustering performance. Also, a new lemma is proposed to provide the formulas about the partial derivation of the trace function with respect to an inner matrix, together with its theoretical proof. Based on this lemma, a gradient-based algorithm is developed to solve the proposed model, and its convergence and computational complexity are analyzed. Experiments on six real-world datasets are performed to show the advantages of the proposed algorithm, with comparison to the existing baseline methods.

Multiview Concept Learning Via Deep Matrix Factorization

Multiview representation learning (MVRL) leverages information from multiple views to obtain a common representation summarizing the consistency and complementarity in multiview data. Most previous matrix factorization-based MVRL methods are shallow models that neglect the complex hierarchical information. The recently proposed deep multiview factorization models cannot explicitly capture consistency and complementarity in multiview data. We present the deep multiview concept learning (DMCL) method, which hierarchically factorizes the multiview data, and tries to explicitly model consistent and complementary information and capture semantic structures at the highest abstraction level. We explore two variants of the DMCL framework, DMCL-L and DMCL-N, with respectively linear/nonlinear transformations between adjacent layers. We propose two block coordinate descent-based optimization methods for DMCL-L and DMCL-N. We verify the effectiveness of DMCL on three real-world data sets for both clustering and classification tasks.